Calculator Inputs
Use the first mode to split a force into components. Use the second mode to rebuild magnitude and direction from components.
Formula Used
From magnitude and angle: Fx = F × cos(θ), Fy = F × sin(θ)
From components: F = √(Fx² + Fy²)
Direction from components: θ = atan2(Fy, Fx)
The calculator first converts any chosen reference axis and rotation direction into a standard angle measured from the positive x-axis. It then resolves or reconstructs the vector using trigonometric relationships.
How to Use This Calculator
- Choose the calculation mode.
- Enter the unit label and preferred decimal precision.
- For magnitude mode, provide force size, angle, reference axis, and rotation direction.
- For component mode, enter Fx and Fy directly.
- Press the calculate button to display results above the form.
- Use the export buttons to download the result summary as CSV or PDF.
Example Data Table
These examples use standard angles measured counterclockwise from the positive x-axis.
| Case | Force (N) | Angle (deg) | Fx (N) | Fy (N) | Quadrant |
|---|---|---|---|---|---|
| Inclined pull | 100.00 | 30.00 | 86.60 | 50.00 | Quadrant I |
| Lift assist | 75.00 | 60.00 | 37.50 | 64.95 | Quadrant I |
| Reverse drag | 120.00 | 150.00 | -103.92 | 60.00 | Quadrant II |
| Downward thrust | 90.00 | 250.00 | -30.78 | -84.57 | Quadrant III |
| Rightward drop | 55.00 | 320.00 | 42.13 | -35.35 | Quadrant IV |
FAQs
1. What does this calculator determine?
It resolves a force into horizontal and vertical components, or rebuilds magnitude and direction from known components. It also reports quadrant, standard angle, unit vector, and balancing force information.
2. Which angle reference does it use internally?
Internally, the calculator converts every entry to a standard angle measured from the positive x-axis. That makes cosine and sine calculations consistent, even when you start from another axis.
3. Can I enter radians instead of degrees?
Yes. In magnitude mode, choose radians as the input unit. The calculator converts that value, performs the component calculations, and then shows the final standard angle in both degrees and radians.
4. Why can component values be negative?
A negative component means the force points opposite the positive axis direction. Negative Fx points left, and negative Fy points downward. The signs help identify the correct quadrant and true vector direction.
5. What is a balancing force?
A balancing force has the same magnitude as the original vector but points exactly opposite. It is useful when checking equilibrium problems, support reactions, and net-force cancellation in mechanics setups.
6. When should I use the components mode?
Use components mode when Fx and Fy are already known from measurements, free-body diagrams, or simulation outputs. The calculator reconstructs the resultant magnitude and direction directly from those values.
7. Does this calculator work for any force unit?
Yes. The trigonometric relationships remain identical for newtons, kilonewtons, pound-force, or custom labels. The chosen unit label is simply carried through the result display and exports.
8. Why do I see a small rounding difference sometimes?
Small differences appear because decimals are rounded for display. The internal calculations still use floating-point precision, so exported values and reconstructed magnitudes stay consistent within practical engineering tolerance.